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STAIRCASE AND HANDRAIL CONSTRUCTION 

PRACTICALLY EXPLAINED, 


IN A SERIES OF DESIGNS. 


J 

M1NARD LAFEVER, 


ARCHITECT, 


AUTHOR OF “ BEAUTIES OF MODERN ARCHITECTURE,” &C. &C. 


with 


PLANS AND ELEVATIONS FOR ORNAMENTAL VILLAS. 


FIFTEEN PLATES. 



NEW YORK: 

D. APPLETON & CO, 






200 Broadway. 










Entered according to the Act of Congress, in the year 1838, 

BY D. APPLETON & CO. 

in the Clerk’s Office of the District Court of the Southern District of New-York. 


















preface. 


pjarssss: ~ <* 

selections of the most useful matter are made for prac 
tical purposes without useless additions ; and conse 
quently place it within the means of operate men 
No novelties nor new theories are introduced but 
constantly keeping in view the immediate dem’ands 
of the patrons of works of this kind, several drawhms 
are given to very materially aid in constructions fn 

frem lV ** haVe P revi °usly been overlooked, which 

ablTapplicat!ons S UmieCeSSar y ex P ence * *"d unprofit- 







PLATE 1 


Is a perspective view of a design for an ornamental 
villa, which is presented as a model to elicit a spirit 
for beautiful and original designs. 



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The ground and second floor plans of Plate 1. This 
design, as here indicated, is to have the kitchen in the 
basement; but should such be objectionable, a kitchen 
may be very conveniently located immediately in the 
rear, on a line with the principal floor. 





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PL. 3 

Is a perspective view of a design for a country resi¬ 
dence, which presents elegance and conveniences 
suitable for a gentleman of respectable circumstances. 





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PL. 4 

Presents the principal and second floor plans for design 
Plate 3, and the principal floor plan, as here indicated, 
is designed to have a kitchen in the basement ; but it 
may be built with all necessary convenience, on the 
rear of the plan, and with the use of the floor ; and 
should such be desired, a plan for such an arrange¬ 
ment would be very readily conceived. 




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11 


PL. 5. 

Pig’s. 1 and 2, Elevation and Plan of a niche, standing in a wall, 
with its ribs, for practice, which are obtained thus: draw the given 
rib A, a quadrant of a true circle, which is equal to the height of the 
niche in the curve, at 6, 8, in Fig. 1, and equal to the depth 6, 7, 
on the plan Fig. 2. B and C, jack-ribs, which are both the quad¬ 
rant of an ellipsis, and have for their plans B C in Fig. 2 ; the two 
latter are described with a trammel, as represented in C. The bevel 
1, 2, and 4, 5, ill B and C, is the same as 1, 2, and 4, 5j in B C, 
Fig. 2. 

Note. —The two last ribs will serve as patterns for the two on 
the opposite side, and save the expense of making expressly for that 
purpose. For taking distances, and moving the trammel, refer to 
Fig. 5, Plate XXI. This, however, is guided by pins moving in 
grooves, which is represented by the large lines in the cross at the 
rib C. 

HIP-ROOFING, FIG. 3. 

To obtain the height, length, and backing of the hip-rafter H, a 
bf e being a plan of the right angled ends, let e cf be the seat of the 
common principal rafters, c d the height of the roof, and e d and d f 
will be the length of the common rafters ; raise g c equal to c c/, the 
given height, perpendicular from a c, the seat of the hip-rafter, draw 
a g , and the line a H g will be the length of the hip-rafter. To 
obtain the backing, draw x z y at right angles to a c, the seat of the 
hip, place one point of the compass on £ and describe a circle to 
touch the rafter, draw w x y to intersect the circle and seat a c at w, 
and x w y will be the planes or backing of the rafter, D will be the 
shape, and one end of the rafter required. 

TO GET THE CUTS OF THE PURLIN TO THE HIP-RAFTER, AND 
LIKEWISE THE JACK-RAFTERS TO THE IIIP-RAFTERS. 

Place the purlin I, at any place in the principal rafter, and at right 
angles to it, take any distance in the points of the compass, and from 
the point h describe the circle p s r q, drop h s square froin the 
rafter at the upper side of the plate, drop p n, s m, li i, r k, and q l, 
parallel to the wall-plate / b, draw k b at right angles* to r k, and 
q l, draw i l , and F will be the side bevel to cut that part li 3 and 
1 2 of the purlin to fit to the rafter ; draw m n to intersect the seat 
at m, draw n i ) and the angle round G will be the down bevel to 
cut the sides h i and 2 3 of the purlin ; and when thus applied to 
the end of the purlin, and cut accordingly, it will make a perfect 
joint to the hip-rafter ; turn a at the end of F down to the dotted 
line and z i l will be the side bevel for the jack-rafter to the hip. 
The bevel A will be the down bevel for the same or jack-rafters. 

All that is necessary to say in relation to the opposite end of this 
plan is, that it is of a parallelogram form, and terminated at its ex- 

* It will only answer at right angles when the plan is square, which is proved at the 
upper end of the plan, which are made parallel to the wail-pla* es - 


12 


tremities by two obtuse, and two acute angles, which consequently 
require the lines g l, r k, h i, s m, p n, l k, and n m, parallel to the 
side walls b /, and b j a , in place of at right angles as in the square 
end. The irregular end has the same letters, and is performed by 
the same process, but will require it on both rafters, and on both 
sides of them. 

TO DESCRIBE A SEGMENT OF A CIRCLE, FIG. 4, AT TWICE UPON 
TRUE PRINCIPLES BY A FLAT TRIANGLE. 

Let the extent of the segment be a b, and its height c d ; let ad 
of the triangle be a hypothenuse line to one half the segment, a e 
a parallel line to c b ; place a pin at ad for the triangle to slide 
against, place a lead pencil at c/, then move the triangle from d down 
to «, and one half the segment will be described ; and the same pro¬ 
cess on the other half will complete the segment. 

TO DESCRIBE A SEGMENT WITH THREE STRIPS TO ANY LENGTH 

AND HEIGHT. 

Make two rods e d, and d /, to form an angle e df, so that each 
may be equal to ad and d b ; let c d be the height—place pins at 
a b , the extremities—place a pencil at d , then move d round each 
way from a to b, and the segment will be complete. A segment 
of this description may be drawn to a great extent with rods, by 
describing it at twice, as in Fig. 4. 

TO DESCRIBE AN OCTAGON, AND RAISE AN ELEVATION FROM IT, 

AS fig’s. 7 AND 8. 

Draw a geometrical square, as at abed; place one point of the 
compass on a , extend the other point to the centre e —let a stand, 
and describe a quadrant of a circle ; proceed thus at each corner, 
and the plan of the octagon will be at ////, $*c. This method 
of raising the elevation will be understood by only noticing that the 
dotted lines are raised from the windows g g g, and angles f f f 
to the same in Fig. 6. 

FIG. 8, TO FIND THE CENTRE OF A CIRCLE, WHOSE CENTRE HAS 

BEEN LOST. 

Let a b be the curve ; take any distance, c d, and at any place on 
the curve a b, in the compass, and describe the circles c d e, c d e, 
and their intersections f f will be direct to the centre, and at the 
intersection of the two radiating lines at g, will be the centre required; 
and may be proved by setting one point of the compass in g, and 
sweeping it round from a to b. 

FIG. 9, TO FIND THE MITRE OF A MOULDING IN AN OBTUSE AND 

ACUTE ANGLE. 

Let the plan or shape of the pannel be a Ac d , draw the inner 
line of the moulding, which is of the same width all round ; draw 


i 





13 


d f to cross at the out and inside angles of the moulding, and d f 
will be the obtuse mitre ; and the same process at a e will make the 
acute mitre. The two bevels will be the cut for the templets or 
mouldings. 


14 


PL. G 

Exhibits a plan of groin arches, designed for brick or stone materials, 
resting on twelve piers, which are represented by the letters A B 
C D, &c. 

It is often the case, that in architectural studies, the student la¬ 
bours under disadvantages at the first examination, for want of refer¬ 
ences to the different parts engaged in the problems which he wishes 
to learn ; therefore I shall continue to give them in all intricate 
drawings. 


REFERENCES TO THE DIFFERENT PARTS. 

ABODE, &c, plans of the piers. 

Fig. 1, Elevation of the centring of the elliptical range, and like¬ 
wise a sectional view of the semi-circled centres. 

Fig. 2, Sections of the covering, or boarding to the elliptical 
range ; (see o o o o o, the ends of the boards.) 

Fig. 3, Sections of the semi-circle range, and likewise the given 
height of the groin. 

Fig. 4, Is a sectional view of the elliptical centring, and an eleva¬ 
tion of the given centre. 

Fig. 5, Is a mould or pattern for determining the groin, or angle 
of the two ranges. 

Fig. 6, Is an elevation of the given rib, or centre, and likewise 
three jack-ribs. 

Fig. 7, Mould or pattern for forming the angle or groin in con¬ 
nection with Fig. 5. 

To erect a number of groin arches, the first thing necessary, is to 
determine the opening and height thereof. For the height, in this 
example, I have taken a semi-circle for the summit, or given height: 
now as the given height is of a semi-circle, and much less span than 
that of Fig. 2, it follows that 2 must necessarily be of an ellipsis. 

In the execution of a brick or stone groin arch, it is necessary to 
erect an entire range of centres, either one way or the other. (In 
this. I have taken those of the greatest span, which is considered 
most practical.) It will be seen that one of these openings are 
covered with boards, and the other has only the plan of the centres, 
(see mno j) q, & c. the plans of the centres.) on which the elevation 
l under Fig. 1 stands. The opening between the piers A B E D G 
H I and K, which is boarded over, is also timbered the same as the 
opening between the opposite piers and letters, it being understood 
that the body ranges or openings are covered with boards or plank 
entire, from one end to the other. It is next necessary to cover the 
lesser openings, consequently it will be necessary to obtain the seat 
of the angle on the covering, to correspond with the angles on the 
plan at the letters abed , for which proceed thus : Divide Fig’s. 2 
and 3 into as many distances as there are boards or plank to cover 
the same, then drop dotted lines from each joint or board perpendi¬ 
cular to the lines a b and c, and from thence continue the same line 
to the diagonal line a d c and a b d, which has the same figures as 


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15 


those on the circular line at Fig’s. 2 and 3, and are likewise the seat 
of the groin or angle. 

To obtain the seat of the angle on the covering of the elliptical 
range, get the stretchout of Fig. 2, from a to b, and place it at any 
convenient place, say Fig. 5, (see the line a b in Fig. 5, which is 
the envelope,) then take the distance e d from the line a b from 
one pier to the other of the capital letters A and B, and set to e d 
in Fig. 5, 5 5, 9 9, &c. and transfer them to the corresponding letters 
in Fig. 5, and then strike a line through all of those points, and it 
will produce the necessary line for the seat of the angle on the 
covering. It will be proper to observe that those parts in the line 
a b Fig. 5, are just equal to the width of the boards in the circle at 
Fig. 2] for a b in 5 is the envelope of 2. 

To apply Fig. 5 to the covering, first, it is understood that Fig. 2 
is the covering: accordingly it will be proper to suppose Fig. 2 
standing on the level a b, and also underboarding ; hence it is evi¬ 
dent that if the pattern at the letters acb d are bent over the board¬ 
ing at a c b d, and marked round accordingly, it will produce the 
seat of the angle required ; to obtain the opposite, just reverse the 
pattern. I have also given Fig. 7 to bend over Fig. 3, which is 
obtained by the same process, and likewise applied in the same 
manner. This, however, is more essential to cut the ends of the 
boards to joint on to the body range, than for any other purpose. 
To cut the boards, it will be observed, that the distances marked in 
Fig. 7 are equal to the boarding in Fig. 3 ; therefore, if they are cut 
according to the circles c d and a d, they will make a perfect joint 
to the boarding of the body range. 

Fiaf. 6 is an elevation of one of the semi-circled centres and their 
jack-ribs, (see the sections at Fig. 1,) / at Fig. 6, is an elevation of 
/ in Fig. 1, g and li in Fig. 6 are also elevations of g 6 in Fig. 1. 
It will be understood that/g- li in the plan, are the seats of the jack 
ribs/g- h in Fig. 6 ; and likewise, that f g h will set on the circled 
sides of the body range, consequently they will require beveling. 
The bevel may be obtained by applying to the sections f g h in 
Fig. 1, where the bevel may be seen at the seat of each section. 

REFERENCES TO THE SMALL LETTERS. 

I in Fig. 1, represents an elevation on the elliptical centre. 

o o o, in l, represents the boarding. 

m n o p, &c. represents the plans of the centres, (see l, elevation 
of centre.) 

ooooo, long side of the piers C F I, represents the boarding. 

abcefghijk, plans. The same letters in Fig. 1, and also 
in 6. 

1 2 3 4 5, &c. by the side of the piers B E H, represents the 
plates. 

N ote ,—it may be understood that abed, at Fig. 5 will answer 
the same purpose as a 8 d in Fig. 5, for they precisely fit each other. 


16 


PL. 7 

Is a plastered groin arch designed for an oblong ceiling, and repre¬ 
sented at its angles by the letters ABC and D. The angle or groin 
ribs in this example, are all connected at the centre of the ceiling; 
consequently it may be termed an entire groin ceiling—whereas, if 
any part of the horizon or centre was horizontal or level, it might 
be termed a groin ceiling with a horizontal centre, which is often 
the case, and affords room for ornamental centre flowers. 

This design may be executed of one, or one and one quarter inch 
boards. 

Note. —It would not be unsafe, to execute a ceiling of this kind, 
of 1^ inch plank, over a span of from 30 to 40 feet, if care should 
be taken in the execution to avoid splits, by nailing in improper 
places. 



TO DRAW THE RIBS TO AN OBLONG PLAN. 

First, determine the height of the ceiling in the centre. In this 
design, the groin rib at Fig. 2, is a semi-circle ; consequently it raises 
one half of the conjugate diameter, (that is, one half of the smallest 
span,) and thus the given rib being a semi-circle, the transverse and 
angle rib required, will be a semi-ellipsis, which may be drawn by 
two methods. In this example I have given both ; one by trans¬ 
ferring lines from the given rib Fig. 2, capital F, to the other two 
ribs, capital F, Fig. 1 and Fig. 4, which is both tedious and incor¬ 
rect in practice ; the other is drawn by a trammel and two strips of 
wood, and represented at Fig. 5. 

The groin rib being got, at Fig. 2, proceed to draw Fig. 1, the 
angle rib. First, divide the semi-circumference into any number 
of equal parts, say seven ; then drop lines from 12 3, &c. perpendi¬ 
cular to the base line B D, to intersect 12 3, &c.; then let the same 
lines extend to the figures 12 3, &c. on the base of the angle rib, 
Fig. 1 ; draw 1 1, 2 2, 3 3, &c. at right angles to the base line B D ; 
take the distance 1 1, in Fig. 2, and transfer it to 1 1, in Fig. 1, and 
so also 2 2, 3 3, &c. to the same figures in Fig. 1 ; and by tracing 
round by 1 2 3 4 5 6 7, one half of the angle rib will be produced: 
and to obtain the other half, proceed the same way. The angle rib 
being drawn direct from one angle of the ceiling to the other, (that 
is, on the middle and thick line between B and C ;) it will be ob¬ 
served that the outer edges of the rib will not be in range with the 
body range, and will not be so convenient to nail the ends of the 
lath : therefore, in order to make the groin perfect, it will be neces¬ 
sary to make the angle ribs to accord in shape with Fig’s. 6, 7 and 8. 
It will also be observed, that the angled recess in Fig’s. 6, 7 and 8, 
are not the same distance in from the two extreme points, which is 
produced by the plan of the groin’s being of an oblong figure; 
whereas, if square, (that is, the same size on all four of its sides,) it 
would be the same. It will be further observed, that it requires 
more on the side C, than on the side B, which is likewise caused by 
C being on the side, and B on the end. 


























































































































































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17 


TO PRODUCE THE INNER CIRCLE THAT JOINS ON THE SIDE AT 

C, AND END AT B. 

First, draw the lesser or inner circle, under Fig. 2, the given rib; 
then take the shorter distances 2 2, 3 3, &c. in Fig. 2, and transfer 
them to the same figures in Fig. 1 ; trace round as above described 
for the outer circle, and the circle required to correspond with the 
angle and body, will be produced. 

TO SHOW THE METHOD OF CUTTING THE BODY RIBS, TO JOINT 

WITH THE ANGLE RIBS. 

First, determine the location of the ribs, say at E F G and H: 
then raise two perpendiculars from the letters j i, in G, to cross tins 
rib Fiff. 4, which, when raised up, will range directly over G ; then 
draw the lines y p , parallel to the base line C D ; now take the 
square and apply it to the Fig’s. 8 9 10; then scribe across from S 
to 9, and the plumb-cut required will be produced. To get the cut 
at the joint, just slide the square out to x y, which will give the cuts 
required. Proceed the same way down at the square 11 12 13, for 
the rib H. 


TO CUT THE JOINT, JOINING ON THE STDE OF THE ANGLE RIB. 

Take the bevel 14 15 16, and apply it to H, the plan of the rib, 
and join the blade 14 16, to the plan of the angle rib A D ; then 
take the bevel and apply it to H, directly over the rib Fig. 4, which 
is the same length of the shortest rib, (see the letters a, b, c, d, e,/, 
in H A, which’shows that if the shortest, rib in Fig. 4 is raised 
perpendicular and set over the plan H, would be in its practical 
position, and also joint to the angle rib.) It must be observed that 
the stock of the bevel must lay on the line 11 q. which is parallel 
to the base, and by applying the stock thus, the blade will not lay 
flat on the under side, but will only touch at the lower and opposite 
corner, but at the same time when thus applied and cut accordingly, 
the joints will be perfect. 


REFERENCES TO THE FIGURES. 

A, B, C, D, plan of the groin. 

Fi°\ 1, Elevation of the angle rib. 

Fig. 2, Elevation of the given rib across the smallest span. 

Fiv. 3 One half of the angle rib in the shape when cut out of the 

board. . 

Fio - . 4, One half of the transverse rib, or rib over the greatest 

Sf> Fig. 5, An Elevation of the single rib drawn by a trammel. 
Fig’s. 6, 7, 8, plan of the angle rib at its butments. 
t u v, w, x , y , represent an elevation of the rib, Fig. 2, when cut 
out’of’the board, and likewise are the same at Fig. 4, in the trans- 

F G H, ground plan of the ribs. In will be noticed that E F 




18 

G H are placed over the elevation of the ribs, which is done for the 
purpose of conveying a proper understanding of them. 

a , b, c, d , e, /, in G H, over the elevation, will correspond with 
the same G, H, in the plan. 

14, 15, 16, bevel applied. 

8, 9, 10, square applied to the horizontal y , j). 

11, 12, 13, square applied to cut the joint of the short rib, to the 
angle rib. 

TO DRAW FIG. 5 WITH A TRAMMEL. 

First, draw the line C B, the base line of the angle rib Fig. 1, in 
the plan ; then get the centre of C B, and raise a perpendicular 
therefrom equal to 7 7, the height of the ceiling at the given rib, 
Fig. 2; then take the height 77, and apply it to the trammel at 1, 
on the circle of the ellipsis, and 2, on the base line ; then the dis¬ 
tance 1 2, on the trammel, will be just equal to 1 2, in the per¬ 
pendicular lines at the centre ; then take the semi-transverse diam¬ 
eter of the line C B, which is from C to 2, and apply it to the tram¬ 
mel from 1 to 4, which is also placed on the perpendicular line 1 4 ; 
now suppose the trammel first located perpendicular, and 1 4 of the 
trammel would be equal to, and on 1 4 on the perpendicular line. 
The trammel or strip being thus placed, fix brad-awls in 2 and 4 in 
the trammel; the black dots represent the awl, and the outer circle 
the handle to the awl, to secure the strips z z ; if for a large span, 
they may be screwed on, and if for a smaller span, brads or small 
nails will answer. To describe the circle from 1 at the centre in 
the horizon, round to C, at the base of the rib, suppose the trammel 
x, to be placed perpendicular on 1 4—apply a lead pencil to the hole 
at 1 ; then move the trammel x round from 1 to 2, minding at the 
same time to keep the brad awls at 2 4, snug to the strips ^ z, and 
one half of the rib will be complete. For the other half, if made in 
two pieces, take the half already obtained, and use it for a pattern 
thereto ; but if required in one entire rib or piece, the two strips ^ # 
should be reversed; then move the perpendicular piece on the op¬ 
posite side of the centre line, and the horizontal piece directly under 
Fig. 5 ; for to describe the ellipsis, proceed as in the above already 
drawn, and the circle C 1 B, will be produced. 

DESCRIPTION OF THE INNER CIRCLE. 

First, it will be observed that the circle b 1 d, is a trifle to the 
right of the centre, which is caused by the plan of groins being of 
an oblong square ; (see the plan of the rib from C to B ; and "the 
greater difference will be understood to proceed at C, from its sitting 
on the longest side ; and at the opposite angle at B, from its sitting 
on the shortest side of the plan.) To make the thing easily under¬ 
stood, a plan of the butments is given at Fig’s. 6, 7 and 8, 
represented by the letters a b c —which will show that this difference 
will be right—the reverse on the opposite side. This inner circle 
is drawn the same way as that of the outer, with no other alterations 





19 


than to take half the distance b d , which is at 3, on the opposite side 
of the line from 2, and set it on 5 on the trammel, just above 4. 
Mow proceed the same way to describe the ellipsis as above directed ; 
for the outer line thus far, produces one side of the angle rib/ For 
the opposite side, the one obtained may answer for a pattern. 

Note. —The transverse is drawn the same as that of the angle 
rib, and is generally represented first, which is, however, a matter 
of no difference, for they are of the same height in the centre of the 
ceiling. Further—if the ribs are drawn and cut as herein described, 
and executed accordingly, it will produce a perfect groin ceiling. 

* This angle rib is made of two planks or boards, as occasion may require, and 
when cut and put together as here represented, will form a complete angle rib. (See 
the Fig’s. 6, 7, 8.) At the centre it will be square. 


20 


PL. 8. 

In this Plate are two scrolls described by the same rule and cen¬ 
tres, but have different proportions. 

These two examples are given in order to show that a scroll or 
spiral fret may be contracted by making the centres smaller, and 
extended by making them larger. 

REFERENCES TO THE FIG’s. 1, 2, 3, 4, 5 AND 6. 

Fig. 1, A scroll of one revolution and three quarters, drawn by 
six centres got by dividing a geometrical square into 36 equal parts. 

Fig. 2, An elevation of the wedges to strain the veneer round the 
block under the curtail step. 

Fig. 3, A part of the riser and veneer, (see riser and veneer in 
Fig. 1.) 

Fig. 4, Plan of a revolution, and a half scroll. 

Fig. 5, Pitch board. 

Fig. 6, Face Mould. 

Note.— In Fig. 1, I have likewise described the block and curtail 
step, which will be explained. 

%• 

TO DRAW THE SCROLL IN FIG. 1. 

First, draw a circle (generally called the eye,) 3^ or 3^ inches, 

(in this it is 3^ ;) then draw a geometrical square equal to one half 
of the eye—divide the geometrical square into 36 equal parts or 
squares, and at the same time extend one of those parts out to 6 ; 
now draw the spiral lines—set one point of the compass on 1, one 
square from the centre o, and extend the other point down to o on 
the edge of the eye—let 1 stand, move o round to 1; let the outer 1 
stand, extend the inner 1 out two squares to 2 ; let 2 stand, move 1 
round to 2 : let the outer 2 stand, move the inner 2 down to 3, move 
2 round to 3 ; let the outer 3 stand, move the inner 3 out to 4 ; let 

4 stand, move 3 round to 4 ; let the outer 4 stand, move 4 out to 5 ; 
let 5 stand, move 4 round to 5 ; let the outer 5 stand, move the inner 

5 out to 6 ; let 6 stand, and move 5 round to 6, and the convex side 
of the scroll will be complete. To describe the inner or concave 
side, follow the same figures back—that is, after setting the width 
of the rail in at 6 6. 

TO DRAW THE BLOCK AND VENEER FOR THE CURTAIL STEP. 

First, set back from the front of the rail at 6, Fig. 1, to I, one 
half of the projection of the nosing, which will be the front line • 

of the bracket or front string; then draw the line I J M N P, by 
following the same centres of the rail, and the concave side of the 
block will be produced. For the veneer and convex side of the 
block, set one point of the compass in 5, and extend the other point 
out to K; let 5 stand, move K round to L, and so round until the 
line or veneer meets the letter A—which is the end of the veneer 
let into the block from P to A, by running in the cut of a pannel 
saw. 




5 






































































































21 


TO FORM TIIE BLOCK, AND WORK IT OUT. 

In order to secure the block from shrinking and breaking apart, 
it is necessary to glue it up into about five thicknesses, (see Fig. 2, 
the riser.*) These thicknesses must be equal in width to the line 
L 20, (that is, the ones that lay across the step,) and those that run 
lengthways the step, equal in width to the line C 21. To prepare 
the^block for the reception of the front string and bracket, cut the 
gain I H D, noticing that the junction of the string and block is at I; 
the letter b is the bracket, and c d e Ha part of the front string ”, 
from the bracket, it will be understood that the block is made suffi¬ 
ciently smooth round to P, not to require any veneer. To get the 
length of the veneer, take a small cord or twine, and apply one end 
at ?he end of the veneer at the letter A—then encircle the block 
from A round by L K to G, which will be the length of the veneer 
required; then calculate whatever thickness for the wedge may be 
thought proper ; (in this it is one half of an inch) from that to 
one inch is proper. It will be understood at the same time from 
Fig. 3, that the lower riser must be in the same piece with the 
veneer. 


TO PREPARE THE. RTSER AND VENEER. 

First o-et the length as above described, then guage the veneer at 
B about 1-Sth of an inch thick; then take a rip saw and cut the 
veneer from A to B, plane it up without the least variation that can 
be seen, crossways, giving it a gradual diminish from B to A, so 
that A may enter the cut of a pannel saw ; then prepare a quantity 
of hot water and put the veneer into it, and there let it lemain until 
it becomes as soft as a piece of leather. Prior to this, take a sizing 
of clue and size the block, and let it get dry before the application 
of the veneer—and at the application give it another good coat of 
well-prepared glue. Then take it and place the end perfectly square 
into the saw cut at A, and gradually bend it round the block, until 
it will admit of the riser’s fitting in the block at E, minding to• have 
it well clued at the same time ; then take the wedges at Fig. 2,;and. 
drive one from the upper side and one from the under side, and the 
wedces being properly drove, will strain the riser smooth and snug 
to the block. Care must be taken to have the veneer lay snug to 
the block from K to B, which may be effected by placing the block 
in some proper place and applying a flat piece across it, and secure 
it by a weight or some other means, in which place it should remain 
until it becomes perfectly dry. 


TO DRAW THE CURTAIL STEP. 

In Fic 1 the dotted lines represented by the letters k Ih n, fyc. 
is tlm outer line of the nosing of the curtail step, and is drawn by 
th ime centres of the rail. 


* And wedges to strain the veneer. 


22 


The dotted line g g at the right hand, is the width of the tread 
of the step from the first rise to the second ; 5 12 is likewise the 
width of the step ; h h, nosing of the second step ; g i, second riser; 
j l k is the return of the nosing round the bracket. In this plan, I 
have extended the nosing over the bracket, equal to the size of the 
bannister, which is not practised by all stair builders, though to me 
it appears most mechanical. 

TO DRAW THE SCROLL FIG. 4 . 

Draw the eye or circle or 3^ inches, then draw a geometrical 
square in the centre, equal to one-third the diameter of the eye, and 
for the other parts, proceed precisely as in Fig. 1. 

TO DRAW THE FACE MOULD FIG. 6. 

Take the pitch-board Fig. 5, and apply the base line 5 12 to the 
convex side of the rail or scroll; then draw the ordinate lines 6, 5, 
6, 6—7, 7, 8, 7—5, 9, 10, 5, &c. perpendicular to the base or under 
edge of the pitch-board 5 12, and extend them up to the hypothenuse 
or rake line 5 13, to intersect the figures 6, 7, 5, &c., then take the 
distance 6, 6, 6, from the line 5, 12 across the eye of the scroll in 
the point of the compass, and transfer them to 6, 6, 6, in Fig. 6, 
(noticing that the ordinates in G are drawn at right angles to the 
rake of the pitch-board.) Proceed the same way with 7, 5, 20, 21, 
&c., and then trace round from 6, 6, to 5, 5, and the size and shape 
of the face mould will be produced. Now to understand the prac¬ 
tical position of the face mould, Fig. 6, suppose the pitch-board, 
Fig. 5, to stand on the line 5 12 across the eye—then it will be un¬ 
derstood that the line 5 13 of the pitch-board is the rake of the stairs. 
Now, if the student observes with attention the pitch-board standing 
as above placed on the line 5 12 across the scroll, he will see that 
the face mould, Fig. 6, will range precisely over the corresponding 
one in the plan of the scroll, Fig. 4. 

Note. —The letters///, #*c. Fig. 1, represent the bannisters. 




















. 















. 




















































































23 


PL. 9. 

This Plate is introduced to show the method of applying a hand¬ 
rail to the stair previous to cutting the joints, or bringing the rail to 
its uniform size and form, which is the course pursued at present 
by the most experienced stairmen, and by whom the most perfect 
rails are executed. The application is as follows:—First, make the 
brackets a a a, as in Fig’s. 1 and 2, and fix them to the stair as at 
a a a, the plan Fig. 1 ; the bracket a is cut open in the middle suffi¬ 
ciently wide to admit the rail to move either way, as required in 
securing it by wedges for cutting the joints, and preparing the rail 
at several points to a proper size : after which, the rail may be taken 
to the bench and prepared for placing upon the ballusters. 

The executor should be very particular in forming the easings in 
the strings and rails ; for in that portion the entire elegance is de¬ 
pendent : and to produce which, the easings must be formed so as 
to intersect with the straight parts perfectly easy to the eye, and at 
the same time to form the curve or circular part, so as not to fall too 
low ; for such would produce as unpleasing effect as short and abrupt 
easings ; it is therefore important that the executor’s judgment be 
properly exercised on this important part of his profession. The 
following are the parts described on the Plate:— 

Fig. 1, Plan of the Stairs ; a a a, the brackets as in elevation, 
Fig. 2. 

Fig. 2, Elevation showing the application of the rail when fitting 
the joints and easings as above described ; a a a, the brackets to 
support the rail as above ; b, a portion of the string joining to the 
second floor ; c, second floor, d , the turn of the rail at commencing 
to ascend the second story flight; e, the easing between the ascend¬ 
ing and level parts of the string ; f, the under line of the string, and 
that portion of the soffit or ceiling, that envelopes the winding and 
circular part of the stairs. 

With the above explanation and the accompanying drawing, the 
executor will be prepared to investigate every part of the subject, so 
as to enable him to perform in execution the most difficult and in¬ 
tricate parts in this branch of his profession, with a greater degree 
of perfection than by the stiff and arbitrary method of lines exclu¬ 
sively, that are laid down in the many excellent works at present 
extant. 

It maybe important further to advise the ingenious young operator 
not to fancy that his knowledge of the rules laid down will enable 
him to make quite as perfect a piece on his bench, as he could by 
the above mechanical process. 


24 


PL. 10. 

As stairs of six to eight inch openings, are the most in use of any 
other kind, there are frequently instances of many being obliged to 
execute them, who are but little experienced in stair-building; con¬ 
sequently, it is thought proper to give the most difficult parts 
engaged therein, in the following practical manner. 

REFERENCES TO THE FIGURES. 

Fig. A, Plan of the rail, front string and nosing: the outer dotted 
line represents the front line of the front string; (that is, the one 
farthest from the centre o, commencing at 1, and terminating at 2:) 
the inner dotted line represents the front line of the nosing on the 
platform. 

Fig. B, Plan of the cylinder put up in staves, glued and screwed 
together. 

Fig. C, The elevation and stretchout of the circular part of the *9 

front string passing over the dotted line 1 2, in Fig. A, with a part 
of the last step of the first flight, and part of the first of the short 
flight going off the platform, and landing on the floor. 

Fig. D, Falling-mould for the concave side of the rail, passing 
over the line 5 7, in Fig. A. 

Fig. E, Convex falling-mould, passing over the outer line 6 11, 
in the plan Fig. A. 

EXPLANATIONS TO FIGURES A, B, C, D, AND E. 

Fig. A, Is the plan of a rail corresponding precisely with the plan, 
letter A, in Plate YI, across the centre O, from 6 to 11; the tangent 
line 13 14, is the same as 13 14, in Plate YI, and is got by the same 
process. The dotted line 15 16, a tangent to the circular dotted 
line, (which is the front string,) is the stretchout of the circular part 
of the string; the line 17 18, is the stretchout of the concave side 
of the rail. 

TO DRAW FIG. B, A PLAN OF THE STAIRS AND CYLINDER. 

First, take the opening of the cylinder and draw it at any con¬ 
venient place, say at Fig. B; then determine the location of the 
joint of the straight and circular part of the string,* say at ah; 
then take any number of staves, (in this design I have given only 
three, of which one is omitted for want of room,) and draw lines 
from the centre O, through the intersection of the two staves at cf } 
and e d , which will give the bevel for working the staves. For 
instance, take a bevel and apply the stock to the dotted line c b, of 
the stave that is connected with the straight string, and the blade, 
on the bevel line c f; then plane up the stave to fit that bevel, and 
so also d c /, and the two staves will stand precisely over the lines 

* 1 have located this 2 and 5-Sths of an inch from the circle, which renders it easier 
to make the intersections of the straight and circular parts perfect, or as near so as 
possible. 


PI,, 10 








































































I 


25 

herein represented by the letters b c, d e, f and g. To work out 
tiie circle, together with the straight part annexed thereto, first take 
a thin piece of board, and make its shape precisely the same as the 
lines b, a, J, c, f and g ; then take the pattern just described, and 
apply it to the end of the stave, and mark round, which will pro¬ 
duce the scribes necessary for working the stave. Proceed the 
same way with the centre stave, which is described by the letters 
c d e and f. 

TO GLUE UP THE STAVES IN THE BEST WAY TO AVOID A VARIATION 

BY SLIPPING OUT OF PLACE. 

First, cut a place in the stave at i, for the reception of a screw, 
then take the screw k, and screw the two staves together, in order 
to make them permanent: two screws will be necessary. By thus 
proceeding, the cylinder may be nearly completed before glued up. 
The workman will also find a convenience in working the rabbit or 
faciae, and bead ; for he may work from both ways : whereas, if the 
whole was glued up, he would find ditficulty, particularly in those 
small openings. 

TO CUT THE JOINT, AND SCREW THE CYLINDER TO THE STRAIGHT 

STRING. 

First, set a guage from the line J b across to the line h i, then 
guage the line h i, then saw the line h i through and through down 
to h, then cut the bevel joint from a into h ; then the stave being 
cut, the same shape will fit at a h and i ; the stave is thus fitted : 
now drive the screws n n, and they being inclined as described in 
the plan, will bring the joint a h to wood and wood. As seasoned 
stuff is important in cylinders, I have made the staves in this ex¬ 
ample only 2\ thick, consequently, it causes a lack of wood between 
/and i : To remedy that, the triangular f i P might be left on the 
straight string: it is a matter of no great consequence whether on 
or omitted. 

Note.—A fter the faciae and bead are completed, then unscrew 
the joints, and put on a sufficient quantity of glue ; then refit them, 
and drive the screws as before, and the joints will be permanent 
and regular. The letter q represents the back line of the bead—r, 
the front side of the bead and faciae, and s, the front of the upper 
faciae. 

TO DRAW THE ELEVATION AND STRETCHOUT OF FIG. C. 

First, take the dotted stretchout 15 16 at the plan Fig. A, and 
raise them perpendicular up to 15 16 on the under edge of the 
nosing of the platform ; then set up from 16 to 19 the height of a 
riser ; then set down from 15 to I the height of a riser. This pro¬ 
duces the stretchout of the cylinder, and at the same time represents 
a part of two common steps. The figures 3 and 4, at the extremi¬ 
ties of the nosing, are just equal to the stretchout of the dotted line 
3 4 in the plan Fig. A, representing the nosing line. 


26 


TO GET THE LENGTH OF THE STAVES. 

First, find the stretchout of the staves round from bale and d, 
and apply them to the dotted lines on the under side of the falling- 
mould, or under side of the elevation of the front string at 1 2 3 4 
5 6 ; then commence at 1, and raise a perpendicular line from 1 up 
to 1, which will be the length ; the width will be from 1 to 2 on the 
horizontal dotted line : for the middle stave, take the perpendicular 
line 3 2 for the length, and the horizontal dotted line 3 4 for the 
width : a a are the joints of the cylinder to the straight string,— 
b b are the joints in the rabbit or faciae, caused by cutting a bevel 
(see the joint in the plan of cylinder) at a h, and it will be seen at 
the bevel joint, by its passing from the letter h out to «, it makes the 
difference of the two dotted lines in crossing the projection of the 
rabbit of the faciae, which is represented by the break in the two 
lines or joints of the cylinder marked a b , to the string in the eleva- 
vation at the intersections of the straight and circular parts. The 
dotted lines 1 1 and 6 6, at the upper and lower ends, represent the 
line b g in Fig. B. 

Note. —Before I proceed any farther, it will be proper to mention 
the peculiarity of a winding or circular rail passing over any num¬ 
ber of elevated steps. 

First, it is known by practical demonstration, that a hand-rail 
raising and winding over any number of steps, terminating in a 
circular cylinder, that neither two of the front and back edges will 
be parallel to each other ; consequently it is evident that the cuts in 
the convex and concave falling-mould will not be parallel to each 
other; if both are cut square to the rake of the falling-moulds, (see 
Fig’s. D and E placed on their envelopes) that they do not run 
parallel over the envelope part, but at the same time run parallel 
down at s s and up at r r, and is also the same distance apart at s s 
that it is at r r, and so also is the under side of the falling-mould to 
the front string, Fig. C. It will likewise be observed, that the four 
lines across the two falling-moulds at each end of Fig’s. D and E, 
are square to the hypothenuse, or rake line of the pitch-boards, and 
parallel to each other ; but the cuts at the centre of the stretchouts 
are not parallel when cut square to the rake or hypothenuse line. 
Therefore, it is a duty that devolves, through the nature of the 
proposals for this work, to explain satisfactorily the mysterious parts 
connected with the various problems or examples that are included 
in this work. The above references and notices are inserted for 
the purpose of placing in view the proper object that will be most 
likely to lead the student to a more direct understanding of them. 

TO DRAW THE CUTS OF THE CONCAVE AND CONVEX SIDE OF THE 
RAIL PARALLEL, AND TO SHOW THE WOOD REQUIRED TO CUT 
THE JOINT IN VARIOUS POSITIONS. 

First, as I have prepared this Plate to complete Plate II, it 
will be observed that the line 22 0 22 across the centre of Fig. E, 
which is the same as the letter C in Plate VI, is cut square to the 




27 


rake or hvpothenuse line of the stretchout. Next it will be seen 
that the concave* mould Fig. D, does not run parallel to Fig. E ; 
therefore, 23 0 23, which is square to the mould, will not be parallel 
to the line 22 0 22 in Fig. E ; consequently, they will not make the 
joint required, although the moulds are both on their inclined planes: 
and to understand the thing perfectly, (see the two small portions 
of the common pitch-boards at the upper and lower ends of the two 
moulds, Fig’s. D and E, that they are raising equal distances at the 
letters 5 5 and r r at the upper and lower ends of the moulds,) now 
to obtain a parallel cut to the outside of the rail, draw the line 22 0 
22 across Fig. D, parallel to 22 0 22, which is square to Fig. E, 
and the parallel cut will be complete; but at the same time will 
not be a square joint in front, as in the back, or convex side of the 
rail. 


TO GET THE JOINT SQUARE IN FRONT. 

First, draw the line 23 o 23 square to the concave mould D ; then 
to make the convex side in Fig. E, parallel to it, draw 23 o 23, in E, 
parallel to 23 o 23, iri Fig. D, and the joint will be complete—which 
is directly reversed to the above. 

TO DIVIDE THE VARIATIONS, AND SHOW DIFFERENT QUANTITIES 

OF WOOD REQUIRED BY THE VARIATIONS OF THE DIFFERENT 

POSITIONS OF THE JOINT. 

First, it is understood that the lines 22 o 22 and 23 o 23, are ex¬ 
plained, and run parallel to each corresponding line in the two 
moulds ; then to divide the difference, divide the distance between 
the two lines 22 and 23, at the ends of the lines, and in the circles 
running through 22, 23, into two equal parts ; then draw the line 
ooo, through the moulds, which will produce the variation, and 
likewise will be square to the centre section of the rail; that is the 
same as to say, draw a falling-mould for the middle black line, run¬ 
ning through the centre o, in the plan of the rail, at Fig. A, which 
is also the centre section of the elevation of the rail. Now to pro¬ 
duce the wood required to cut the joint, when executed in either 
of the three positions represented by the lines 22 o 22, ooo, and 
23 o 23, drop lines from each intersection of those lines, to the upper 
and under edge of the falling-mould, Fig’s. D and E, down to the 
plan of the rail at Fig. A, and the over-wood for either will be pro¬ 
duced at the three lines at the right and left of the line o o o o o, 
round perpendicular through the axis of the cylinder or well-hole. 
The three lines each side are represented at the radiating lines 1 2 
22 22 3 4, drawn from the convex side of the rail A. This, as above 
observed, must pass through the intersecting of the lines at the upper 
and under edge of the rail, or falling-moulds D and E. 

* Meaning the inside of the rail in the circular part, for the same side of the rail in 
its straight parts might properly be termed the outside, for the well-hole is the outside 
of the stairs; but any diminution towards the axis or centre of a cylinder or circle, 
will be coming into the centre; consequently, the concave mould will be the inside 
mould to the circular part. 


28 


PL. 11. 

STAIR RAILING OVER A SMALL OPENING. 

To furnish such drawings and explanations of the several parts 
of stairs as can be comprehended by workmen, not versed in science, 
nor much experienced in the stair department, and as will enable 
them to execute with a considerable degree of accuracy, it is neces¬ 
sary to study simplicity, both in the drawings themselves, and in 
the terms used for their explanation. In what follows, I shall aim 
to do this, even if it be at the occasional sacrifice of that verbal 
polish, and that scientific arrangement and explanation, which a 
learned reader might desire. 

THE PLAN OF THE SEMI-CIRCULAR PART OF A STAIR-RAIL BEING 
GIVEN TO OBTAIN THE CONVEX FALLING-MOULD. 

Let A C E F H J (Fig. 1the plan of the semi-circular part 
of a stair-rail, having a portion of straight rail attached to it; with 
the diameter, G I, of the convex side of the plan for radius, and 
from the points G, I, as centres, describe arcs cutting each other at 
P, and join P I, P G ; bisect the arc I H G in H, and through H 
draw a tangent, K H L, of any length, and produce the lines P I, 
P G, till they meet the tangent: the part Iv L, cut off by P I and 
P G produced, is the extension or stretchout of the convex side, 
I H G, of the plan. Draw the line c e (Fig. 2) equal to the tangent 
K L, and at e, in the base c e , erect a perpendicular, e f equal to 
the height of a step, and join cf; at each end of the hypothenuse 
c fi apply the pitch-board of a common step in the manner exhibited 
in Fig’s. A and B, and make r b or q y in the pitch-board a b c, and 
f u in the pitch-board f g h, each equal in length, I J or D E, of the 
straight part of the rail : making allowance for the easings at c and 
f the line a c f h, formed by the hypothenuse c /, and the upper 
edges of the two pitch-boards, is the lower edge of the required 
convex falling-mould, of which the part q c f i is all that is required 
in this instance. On each side of the angles c,jT, in the lower edge 
of said mould, set off any number of equal parts, say six or eight, 
and from that point of division which is nearest the angle on one 
side, draw a straight line to that point which is farthest from the 
angle on the other side ; do the same from all the other points of 
division, and by the intersections of these lines, obtain the easings 
at c and f; parallel to the lower edge thus completed, and at what¬ 
ever distance may be fixed upon for the width of the mould, draw 
a line for the upper edge, and the required convex falling-mould 
(Fig. C) will be completed. 

The line l m n (Fig. C) represents a butt-joint, and C v, or H v, 
(Fig- 1). shews the over-wood necessary for cutting said joint, and 
are obtained thus : at the point H, (Fig. 1) in the tangent K L, erect 
a perpendicular, and produce it so as to cross the convex mould C; 
bisect the part, « z, which crosses the mould, and through the point 
of bisection, m draw l rn n ; at right angles to the hypothenuse c f 


pi.u 












































































29 


and from n , let fall a perpendicular, n v, upon the tangent K L : as 
already stated, the line l m n represents a butt-joint in the centre of 
the semi-circular part of the rail, and C v, or H v, (Fig. 1) is the 
width of over wood required to cut it; for which overwood, allow¬ 
ance is made in Fig’s. 4, 6, &c. 

Figures 3 and D represent the stretchout and falling-mould ol the 
concave part of the plan at Fig. 1, and are obtained in the same 
manner as Fig’s. 2 and C ; the base c e (Fig. 3) being equal to the 
tangent M N at Fig. 1 ; e /, equal to the height of a riser ; q y and 
f u , equal to the same portions of straight rail as in Fig’s. 2 and C; 
and so forth. It will be perceived, that the two falling-moulds 
(Fig’s. C and D) have different angles of inclination ; that the line 
l m n, in order to be parallel to l m n in Fig. C, (which it must be,) 
cannot be at right angles with the hypothenuse c /, as in Fig. C; 
and lastly, that straight lines drawn across the mould C and D, at 
right angles to the base c e, will have unequal lengths, those cross¬ 
ing D being necessarily the longest. This fact must be particularly 
attended to by stair-builders, if they would construct hand-rails in 
the best possible manner. Even where attention is paid to it, some 
difficulty is experienced in the application of the moulds, and in the 
construction of the rail. Mr. Coulter, of Pliladelphia, recommends 
the method of dividing the difference in the width of the two falling - - 
moulds into two equal parts, and lowering the concave side of t'he 
rail a distance equal to one of these parts, at the same time that the 
convex side is elevated a distance equal to the other. This method, 
though liable to some trifling objections, is doubtless the best that 
has been devised. It will not, however, make an inelegant rail, if 
the convex side be elevated a distance equal to the whole difference 
in the width of the falling-moulds, without lowering the concave 
side at all. I will just add that, further on, will be found drawings 
and explanations adapted expressly to this case ; and to these the 
student is referred for what further aid and information he may re¬ 
quire. 

THE PLAN BEING GIVEN, TO OBTAIN THE FACE MOULD OF A STAIR 

RAIL, WHICH, WHUN PLACED OVER THE PLAN AT A PROPER. 

ANGLE OF INCLINATION, WILL COINCIDE WITH THE SAID PLAN, 

PART WITH PART. 

Let Fig. 1 be the given plan, as before, and draw A B v v I J, 
(Fig. 4) equal to that part of Fig 1 which is represented by the 
same letters ; join the ends of the dotted curve passing longitudinally 
through the centre of the semi-plan at Fig. 4, by the straight line 
w w ; through the point A, and parallel to w w, draw a straight line, 
x A x, of any length, and parallel to it, draw another line, y y, of 
indefinite length, so as to touch the convex side of the semi-plan ; 
through the point J, draw a straight line at right angles to the tan¬ 
gent y y, and produce the said line through J and said tangent, till 
they meet in the point y ; through the middle point, w, of the end 
of the circular part of the semi-plan, and at right angles to the 


30 


straight line w w : draw the line n s n, of any length, and make the 
part 5 n (Fig. 5) equal to s n in Fig. 2 ; through n, (Fig. 5) draw 
the line z n y, (which line is the hypothenuse of the triangle z y y, 
and shews the rake or inclination the face mould is to have,) and 
through the points A, I, B. &c. in the semi-plan, and at risdit angles 
to the tangent y y , draw the lines A A, 9 9, $*c. meeting the hypo¬ 
thenuse z y in the points A, 9, tj*c. ; at the points where they meet 
said hypothenuse, erect the perpendiculars 9 I, 6 5, &c. (Fig. 6) 
making them equal to 9 I, 6 5, &c. in Fig. 4, and the parts 6 B, 7 4, 
&c. in Fig. 6, equal to the similarly named parts in Fig. 4 ; through 
the points thus obtained, trace the curves J I v, A B v, and you will 
have the face mould required. 

TO APPLY THE FACE MOULD TO A PLANK FOR GETTING OUT A 

RAIL PIECE. 

Let the oblong 1, 2, 3. 4, (Fig 7) represent the upper side of the 
plank; 2, 5, 6, 3, the thickness of the same ; and 5, 8, 7, 6, the 
under side. Take the face mould (Fig. 6) and apply it, as at Fig. 7, 
keeping the end v v as far from the edge of the plank as is indicated 
by Fig’s. 4 and 6, and tracing out its shape A J v v ; take the pitch 
bevel A at Fig. 5, (which shows the angle of inclination that the 
rail is to have ) and apply it as at A and A ; (Fig. 8) make the 
plumb-cuts C C, A A, across the edge, and also the perpendicular c v 
on the under side of the plank, equal to c v on the upper side, and 
then, applying the face-mould again, as at Fig. 9, complete the out 
line for cutting the rail-piece. 

TO APPLY' THE CONVEX AND CONCAVE FALLING MOULDS TO A 

RAIL-PIECE. 

When the rail-piece has been cut out, as just described, take the 
convex mould Fig. C, (which is supposed to be made of pasteboard) 
and apply it to the convex edge of the rail-piece at Fig. 7, bending 
it round so that the points p, o, 3, in the upper edge of the mould, 
may coincide, each with each, with the points J, I, v, in the upper 
side of the convex edge of the rail-piece, and so that the lines p q, 
o c, 3 //., drawn across the mould 0 at right angles to its base, c e, 
may tally, each to each, with the plumb-cuts A A, B B, C C, made 
on the concave edge of the rail-piece, and continued across the 
under side to meet the above mentioned lines. Having applied and 
bent round the mould in this manner, trace lines along its upper 
and lower edges, and you will have the outline for finishing the 
convex side of the rail. 

In the same way, apply the concave mould D to the concave edge 
of the rail-piece, making the straight part, p o, in the upper edge 
of the mould, coincide with the straight part, A B, in the upper 
concave edge of the rail-piece ; and thus far, the two falling moulds 
will have the same angle of inclination. To find what inclination 
to give to the circular part of the concave mould D, from the point 
n, in the lower edge of the convex mould C, (which is supposed to 


31 


be bent round the convex edge of the rail-piece,) square across the 
under side of the rail-piece, and from the point 2, (Fig. D) where 
the line thus squared across is supposed to meet the lower concave 
edge of the rail piece, draw the horizontal line 2 4, from 2, in the 
line 2 4, set off 2 z, equal to the overwood for a butt-joint, and z 
will be that point in the concave edge of the rail-piece, on which 
the middle point in the lower edge of the circular part of the mould 
D, will rest. Now trace the outline for completing the concave side 
of the rail. Observe that the difference in the length of n 2 in Fig. 
C, and n 2 in Fig. D, represents the difference the two falling moulds 
will have in their angle of inclination. 


32 


PL. 12. 

This Plate exhibits the plans and elevations of the front and back 
strings of a circular stair. The arc A (Fig. 1) represents the plan 
of the front string, or string adjacent to the opening, and C, the plan 
of the string contiguous to the wall. B and D are the stretchouts 
of said arcs, and the several divisions in them correspond, in loca¬ 
tion, with the several divisions made in A and C by the dotted radii, 
which, from the centre O, pass through the front of each step to the 
plan of the back string. In the plans A and C, a. b, c, &c. represent 
the wedges supposed to be inserted on the convex side of the two 
stair-strings, and made to penetrate to a greater or less depth, and 
to be a greater or less distance apart, according to the greater or less 
extent of the circles in which the strings are spirally to wind. In 
this example, the wedges in the front string are made to reach to 
within about an eighth of an inch (see the scale at bottom) of the 
concave side, and to be about seven-eighths of an inch apart; while 
those in the back string only come within about a quarter of an 
inch of the concave side, and are about an inch and a quarter apart. 
The wedges may be shorter and further apart in the back string 
than in the other, for the reason that the back string winds in a 
larger circle than the front one, and of course has a less prominent 
curvature. The depth to which the wedges penetrate, and their 
distance apart, must be left to the discretion of the workman. Care 
must be taken that they be not too far apart, for if they are, the con¬ 
cave sides of the stair-strings will present a succession of plane sur¬ 
faces and angles, instead of that regular curvature which they are 
intended to exhibit. 

Fig’s. 2 and 3 represent the elevations of the front and back strings, 
and are obtained by a process so very similar to that by which the 
falling moulds in the preceding plates are found, that no explanation 
will be necessary. 

In Fig. 2, c represents a separate piece, intended for insertion, at 
its upper edge, into a groove to be made in the under edge of the 
front string, after it has bent to its true shape, and has become en¬ 
tirely dry. In the same way a separate piece may be inserted into 
a groove in the upper edge of the back string at Fig. 3. The line a 
(Fig. 3) shews the width of the skirting when got out separately, 
and the line b is the width of the back string and skirting, when 
they are got out in one piece. When got out in one piece, channels 
or mortises are made in it, for admitting the ends of the treads and 
risers. Whether the strings be mortised for inserting the ends of 
the steps, or whether it be notched, a pitch-board must be applied 
to it, and lines traced for the treads and risers ; but the places for 
the ends of the steps must not be cut out until the string is bent, 
wedged and dried. 

To give the strings of a circular stair their proper curvature and 
spiral twist, make, for each string, a cylindrical block, that is, make 
two frames with battens, or narrow strips of board, nailed on longi¬ 
tudinally, and rounded off at the outer edges, so that each frame 





PI.12 


11 iiffurits .Lilli.A'. )'. 


I 


I 


1 


u ( e 





































































33 


shall, following the outline of the battens, be cylindrical, and have 
the respective curvatures of the circular wall and well-hole. Around 
these cylindrical frames bend your stair-strings, gluing in the wedges 
as you proceed, and, if you please, gluing a piece of coarse canvass 
over the wedges. 

Note.— In making the apertures for the wedges on the convex 
side of the strings at Fig’s 2 and 3, care must be taken to cut them 
at right angles to the stretchout D, (or any other horizontal line,) 
instead of cutting them at right angles to the edges of the elevations. 


34 


PL. 13. 

HAND Railing. Hand-railing is the art of forming hand-rails 
by moulds according to geometrical rules. The principles upon 
which this art depends, are that of cutting a right prism through 
any three given points in space, and that of forming a develope- 
ment of any portion of the surface of the prism. 

In order to illustrate this, let the interior surface of the sur¬ 
rounding wall be that of an entire cylinder, and let the breadth of 
the steps be divided into the frustrums of equal and similar sectors, 
and let the heights be all equal, as is universally the case; then, if 
an interior cylindric surface be erected concentric with the wall 
and the ends of the steps or surfaces on which we tread, and the 
planes of the risers tending to the axis be supposed to meet the in¬ 
terior cylindric surface, it is evident that if the portion of the inter¬ 
cepted surface contained between the indented line formed by the 
ends of the steps, and the circumferent line at the base, be developed 
or stretched out, all the points of the indented line formed by the 
outward or salient angles, will be in the same straight line, and all 
the points formed by the inward or re-entrant angles, will be in 
another straight line. It is also evident, that this will not only be 
the case with cylinders, but with cylindroids, and every other de¬ 
scription of prism ; that is, the points of the development of the in¬ 
dented line will always have such a position, that two straight lines 
parallel to each other may be drawn through the whole number of 
points. 

The points of concourse of the salient angles are called the no¬ 
sings of the steps. 

The line drawn through all the nosings of the steps, is called the 
line of the nosings. 

Now let the portion of the cylinder before uncovered, be again 
enveloped, the development in this case becomes an envelope, and 
the line of nosings becomes an uniform helix, which would be the 
form of the rail for such a stair. 

In this case it would be easy to execute the rail to any length we 
please, in equal portions succeeding each other ; for as the curva¬ 
ture of the helical line is every where the same, the same moulds 
which are used in the formation of one piece, would serve for every 
succeeding piece. 

The steps placed around the circular part are termed winders ; 
in these the risers tend to the axis of the cylinder. 

Steps which have their treads the same breadth, are termed fly¬ 
ers ; in these the risers are all parallel. 

Very few staircases are however entirely circular, but those of the 
semi-circular form, with winders in the semi-circle, and flyers be¬ 
low and above, are very numerous ; in such the line of nosings 
would be crooked, and would form an angle at the junction of the 
flyers and the winders, and that round the semi-circle would be a 
a helix, consisting of half a revolution. 

In the development of the steps, the line of nosings would con- 


I 


PI. 13 

















































































35 


sist of three straight lines, the two straight lines through the nosings 
of the flyers would be parallel to each other, and each extremity of 
the middle one would join one extremity of each of the .other two ; 
the angles are commonly taken away by introducing a curve in 
their places. 

A hand-rail, however, is not a mere helical line, but a solid, which 
may be contained between two concentric cyllindric surfaces, or 
concentric prismatic surfaces. The principles are the same, what¬ 
ever be the form of the plan. A solid erected upon any plan, is 
called a prism ; a cylinder is therefore a round prism, and a cyllin- 
droid an elliptic prism. A hand-rail may stand upon a circular 
base, or partly circular and partly straight, or upon an entire^ellip- 
tic base. In the construction of hand-rails, all prisms are excluded 
which consist of plain surfaces, or, which is the same thing, where 
the sides of the plan consist entirely of straight lines, as in such 
cases, the rails themselves are either straight," or partly curved and 
partly straight from the top and lower sides only, the sides beino- 
in vertical planes. 

We shall therefore confine ourselves to prisms that stand upon a 
circular base, or upon an elliptic base, or upon a base that 1 is partly 
circular and partly straight, or, lastly, upon a base that is partly 
elliptical and partly straight. These two last may be saidjto have 
compounded bases or plans, and the former two simple bases or 
plans; let us call such a prism a curved prism. 

The plan of any curved prism is understood to be of the same 
breadth, and consequently the solid erected thereon will be every 
where of the same thickness. The prism may therefore be a hol¬ 
low cylinder, or a hollow cylindroid, or a concave body partly cy- 
lindricand partly straight; the latter may be open on one side, and 
may have the four planes which join the curved surfaces parallel 
to each other, and tangent to each of the cylindric surfaces. 

Let us therefore suppose such a prism as that last mentioned, and 
let us suppose it to be cut entirely through its vertical surfaces, in 
such a manner that any point in the surface of division may coin¬ 
cide with a straight line every where perpendicular to the external 
prismatic surface, then, every such line will be parallel to the plane 
of its base, and those lines in the cylindrical part of the prism will 
tend to the axis. Now it is evident, that the cut or dividing surface 
will not be a plane, but will wind or twist between the cylindric 
surfaces. It is also evident, that the cut may pass through a line 
drawn in any manner we please, in one of the prismatic surfaces; 
or, that the development of this line may have any degree of cur¬ 
vature in the whole length, or in any portion of the length, or may 
even be a straight line. One of those being supposed to be the case, 
let the upper part of the prism be taken away, then the upper surface 
of its remaining part will be brought to view ; let a line be drawn on 
the exterior surface, parallel to the arris, and another on the concave 
side, parallel to its arris ; and let another cut or dividing surface 
be made to pass through the two lines thus drawn, and let the up¬ 
per part be removed by this division, then the part thus removed 


36 


will form a solid helix or kind of half screw, which may be either 
uniform in its upper and lower surfaces, or have any degree of cur¬ 
vature in any part that may be required, according to the develop¬ 
ment before mentioned. This is the form of the rail for such a 
stair, but to form the solid helix, without cutting it, from a hollow 
curved prism, is the thing required to be done in hand-railing. 

Now, seeing that two of its sides are actually cylindrical, and 
would be vertical if placed in position ; and that the other two 
winding surfaces may be formed to any development we please; 
let us therefore take any determinate portion of the helical solid, as 
a quarter of a revolution, or perhaps something more, as occasion 
may require, and endeavour to form such a portion or wreath out of 
a thin plank, instead of cutting it from a solid curved prism. Be¬ 
fore this can be done, it is necessary to understand the principle of 
cutting a prism through any three fixed points in space, by a plane 
passing through these points ; the points may be in the surface of 
the prism itself, and may be either all in the concave side, or all in 
the convex side ; or partly in the concave side, and partly in the 
convex side :—That such a supposition is possible will readily ap¬ 
pear, since any three points are always in the same plane; and, 
therefore, the plane may cut the prism through any three given 
points. 

The three points through which the section is cut, are said to be 
given, when the seats are given on the plane of the base of the prism, 
which plane is understood to be at right angles to the axis of the 
prism, and when the distance or heights from the seats to the points 
themselves are given. 

It is always to be understood, that the three seats are not in a 
straight line, and consequently the three points themselves not in a 
straight line. 

The seat of a point in space on any plane, is that point in the 
plane, where a perpendicular drawn through the point in space, 
cuts the plane. 

This being established, we shall proceed to shew the best means 
of applying these principles to hand-railing. 

In the helical solid, the winding surface connecting the two 
prismatic surfaces, was defined to be of such a property, as to coin¬ 
cide with a straight line perpendicular to the exterior prismatic 
surface, and consequently, if the axis of the curved prism be per¬ 
pendicular to the horizon, every such line will be parallel to the 
base ; now, let the seats of three such lines be given on the plan, 
viz. let each extreme boundary be one, and let another be taken in 
the convex side, passing through the point which would give the 
middle of the development of the said side of the plan ; the three 
seats would be terminated by the convex and concave sides of the 
plan, and will always be perpendicular to the convex side, and 
equal in length to each other. Let us call the three level lines, of 
which their seats are given, the lines of support; let a plane be laid 
on the three lines of support, the plane will either rest upon three 
points or upon one of the said lines and two points ; it is evident 


37 


that the points which come in contact with the plane, will be at one 
extremity of each line of support; let each of these points which 
come in contact with the plane thus posited, be called a resting 
point. The three resting points are the three points in space, 
through which the plane is supposed to pass, that cuts the curved 
prism. 

Now, because, that each line of support has two extremities, there 
will be six extreme points in all, but as only three can be resting 
points, unless the plane coincides with one of the lines of support, it 
will be proper to shew, which three of the six are the resting points. 
Let the plane, thus laid upon some three extremities of the lines of 
support, be continued to intersect the base of the curved prism, then 
the nearest extremity of the seat of any line of support to the inter¬ 
secting line, is the seat of the resting point of that line. 

For this purpose let a development of the convex side of the rail 
be made according to the plan and rise of the steps. The part of this 
development that is made to bend round the convex or concave cy- 
lindric surface of the helical portion or wreath, is called a falling 
mould, which is supposed to be brought to an equal breadth through¬ 
out its length. Only one falling mould is used in the construction 
of hand-rails. Let, therefore, the falling mould for the convex side 
be constructed, and let two straight lines be drawn from the ends 
of the upper edge of that part of the falling mould corresponding to 
the ends of the wreath, perpendicular to the base of the whole de¬ 
velopment ; also, let another intermediate line be drawn parallel 
to the other two, so as to bisect the part of the base intercepted 
by the said two parallels: the three parallels will thus give the 
heights of the three resting points, the shortest height is at one 
extreme, and the longest at the other. Suppose now, the shortest 
of these three heights taken from each of the three, and the remain¬ 
ders taken at heights, instead of the whole, then the height of the 
first resting point will be nothing, and will therefore coincide with 
its seat; then, if the middle height be less than half the length of 
the remaining height, the seats of the resting points will be the first 
and second extremities of the first and second lines of support taken 
on the convex side, and the extremity of the third on the concave 
side. The first resting point is a point in the intersection of the 
plane of the base with the inclined plane. 

The process is now completely reduced to that of finding the sec¬ 
tion of a prism through three given points, which suppose to be 
done, and the plane of section will touch the supposed wreath, at 
the resting points of each line of support, without cutting the 
wreath of any such line—then, the three lines ot support will be on 
the same side of the plane, viz. on the under side. Let us suppose 
now, another section taken ,below, and parallel to the former, so 
that the wreath may be just contained between these parallel sec¬ 
tions, or planes ; the distance between the two sections will repre¬ 
sent the thickness of the plank. 

The section of the prism through its vertical surfaces, is called 


38 


the rake,"or the rake of the plan : and a mould being cut to the 
rake, is called the face mould. 

The above are the general principles ; the particulars will be 
best understood by the explanations which accompany the dia¬ 
grams in the Plate, and the following engravings. 

Let fig. 1, No. 1, in the Plate, be the plan of a geometrical stair, 
with eight winders in the semi-circle, and flyers above and below ; 
the first or lower steps being denoted by the scroll a ; let ql p m r 
be the plan of the part of the rail that is to be formed in two wreaths; 
and q l and m r straight parts; in order for the better securing of 
the wreaths to the straight parts opposite the flyers. 

Let fig. 1, No. 2, be the development of twelve steps, including 
that of eight winders, two flyers below and two above; D B being 
the base, and B C the height. In the base D B, No. 2, L P M is 
the development of Ip m, No. 1, and L D, M B, the breadths of 
two steps corresponding to the plan. In the height B C, N O is 
the height of the winders, and N B, O 0, each the height of two 
steps answering to the flyers at each end. D E F C, is the line of 
nosings ; the parts D E, F C, of the flyers, being parallel to each 
other, and joined by the part E F, the development of the winders ; 
G R H, and I S K are curves tanged by the straight lines E D, 
E F, and F E, F C, at the points G, H, I, K, or rounded off, as 
shewn at No. 3, on, a longer scale, so as to form an agreeable curved 
line without angles. 

The line G R H I S K may be called the line of the rail, being 
of the same form as the line bisecting the breadth of the develop¬ 
ment of the rail, for the one may be supposed to be every where of 
the same height from that of the other, and therefore, the line 
GRHISK, may be conceived to be the development of the rail. 

No. 3 shews the manner of drawing the tanged curves G R H, 
and IS K; No. 2 the upper one I S K, being the same as the lower 
one G R H, but inverted. 

No. 2 shews more lines than are wanted in practice, in order to 
shew the connexion between the development of the steps, and the 
development of the line of the rail. But, as the development of the 
line of the rail is all that is wanted, make a b, No. 4, equal to the 
height of the winders, draw a c and d b , at right angles each with 
a b ; make a c and 6/each equal to the development of Ip ox pm, No. 

1 ; make e c, and f d , the breadth of a step ; draw c g and d k 
parallel to a b ; make c g and d k each equal to the height of a 
step ; join eg f k and ef ; make e h equal to eg, and ft equal to 
/ k, and draw the tanged curves g r h and i s k as before ; then 
gr hi sk, will be the line of the rail, as in No. 2; for ef will be 
obtained, equal to EF, No. 2 ; and el g will be the section of a 
flyer at the lower end, and f d k the section of a flyer at the upper 
end. The breadth of the falling mould, in common cases, is about 
two inches, therefore, two lines being drawn parallel to the line of 
the rail, each at an inch distance from it, gives the complete falling 
mould for both wreaths. The two parts of the falling mould, as 


39 


divided by a b, are equal and similar to each other, and would there¬ 
fore coincide if applied together. 

Let fig. 2, No. 1, be an enlarged plan of the rail, of double di¬ 
mensions to No. 1, fig. 1, in order that the moulds may be more 
exactly obtained, and the construction more clearly seen. Let A 
B C D E F G, fig. 2, No. 3, be the plan of the part of the wreath to 
be formed, A G being the seat of the line of support at the lowest 
part, and D E that at the highest part: then A is the seat of the 
resting point of the lowest end, and E that at the highest end. 
Take the point C, between A and D, so that C, in the development 
of the line A B C D, may divide the said development in two equal 
parts. 

Let A B C D, fig. 2, No. 2, be the development of the curve A B 
C D, No. 3 ; the parts A B, B C, CD, being the respective devel¬ 
opments of A B, B C. C D, No. 3. In No. 2, draw D K perpendicu¬ 
lar to D B ; and make D K equal to the height of eight steps ;draw 
K S parallel and equal to D If ; join B S ; produce K S to T, and 
D B to V; make S T and B Y each equal to the breadth of a step ; 
draw T U and V W parallel toDK; make T U and Y Wequal to 
the height of a step ; join YV B, B S, S U : then W B S U is the line 
of nosings. The whole is completed as in No. 3, fig. 1. Draw 
A X parallel to K D, cutting the upper side of the falling mould at 
X; draw X Z parallel to A D; produce K D to Z, and let K D 
cut the top of the rail at I; through C draw Y J, parallel to D K, 
cutting the top of the rail at J, and X Z at Y ; then Y J and Z I, 
respectively, are the height of the resting points, whose seats are C 
and E No. 3. In No. 2, draw J R parallel to B D, cutting D K at 
R. In No. 3, join the seats E and C of the resting points and pro¬ 
duce E C to L. In J R, No. 2, find the point O, by making R O 
equal to E C, No. 3 ; join I O, and produce I O to meet X Z at Q,. 
In No. 3, make E L equal to Z Q,, No. 2, and join A L ; through G 
draw tl K, perpendicular to A L, and produce L A to B ; through 
E draw E i parallel to L H,cutting HKat I; make I i equal to ZI, 
No. 2, and join H i, and produce H i to k. To find any point in the 
curve of the section, take any point M in the boundary of the plan, 
and draw M p parallel to E t, cutting H i at p and H I at P ; draw 
p> 7 n at right angles to H i and make p in equal to P M, andm is a 
point in the boundary of the rake. In like manner, let M P cut the 
concave side of the plan at N; in p m take p n equal to P N, and n 
is a point in the concave side. A sufficient number of points being 
thus found, draw a mixed line, ctbcde f g, through the whole and 
a b c d ef g, is the figure of the rake. For greater accuracy and 
despatch, it will be necessary to find a point in the rake correspond¬ 
ing to the extremity of every straight line in the plan, as shewn by 
small letters of the same names as the capitals on the plan. The 
part A B F G being a parallelogram on the plan ; the correspond¬ 
ing part a f b g , on the section, is also a parallelogram ; in this case 
it will be only necessary to find the points «, g,f. Join a g and 
g f ; draw a b parallel to g f\ and f b parallel to g a , and the point 
b gives the commencement of the convex curve bed and the point 


40 


f that of the concave curve. It remains to be shewn that H L, No. 
3, is the intersection of the plane on which the section of the prism 
is formed ; for the point A is not only the seat of the lowest resting 
point, but the resting point itself. A is therefore the point in the in¬ 
tersection of the cutting plane. In No. 2, draw O a parallel to K 
Z cutting B Z at a ; conceive the triangle I Q, Z to be removed to 
to No. 3, so that the point Z may be upon E; and because R O A 
Z is a parallelogram, a Z is equal to R O, and R O is equal to E C 
by construction; therefore the point a will fall upon C: and by 
construction the point Q. will fall upon L. Conceive the triangle, 
with its base, thus coincident with L. E, to be raised perpendicularly 
to the plan; I will be the resting point over E and O the resting 
point over C ; therefore the points I and E will be in the plane of sec¬ 
tion, and consequently be the straight line I O Q,; but the point Q, 
now supposed to be coincident with L, is common to the plane of 
the base; and the plane of section Q, is therefore a point in the in¬ 
tersection of the cutting plane and the base. The point A has like¬ 
wise been shewn to be a point in the intersection ; therefore the 
straight line H L, passing through the points A and L, is the inter¬ 
section of the cutting plane, with the plane of the base. The point 
L, No. 3, will be obtained also by a fourth proportional to I R, I Z, 
R O, or Z a No. 1, setting it from E. to L. 

A mould being cut to the form of the section, as here obtained, is 
called by workmen, the face mould , which we shall suppose now 
to be made. 

To find the Thickness of the Plank, out of which the Wreath 
is to be cut. —Let Z I, No. 2, cut the under edge of the falling 
mould at e , transfer Z £ upon K k, No. 3, from Iv to s : then the 
nearest distance between the point s and the straight line H k, is 
the thickness of the stuff at the upper joint. 

The wreath, when formed into two prismatic surfaces, and into 
two winding surfaces, is said to be squared. This formation is all 
that is required from geometrical principles. Then, supposing the 
wreath set in its proper position, every section made by a vertical 
plane, perpendicular to the convex side of the plan, will be a quad¬ 
rilateral with its two vertical sides parallel, and at right angles to 
the upper side, and at oblique angles to the lower side. This arises 
from the top being so formed as to coincide in every part with the 
line perpendicular to the prismatic surface as defined, and the lower 
winding surface by guaging upon each cylindrical surface from the 
top. 

To draw the Rake on the Slides of the Plank , in order to plumb 
the two sides of the Wreath. —Let A B C D, fig. 3, No. 1, be a de¬ 
velopment of three sides of plank ; let A E, H D, be the top; E F, 
G H, the edge; in breadth equal to the thickness of the stuff ob¬ 
tained from No. 3, and F B, C G, the under sides ; let the lines E H 
and F G be parallel to k H, fig. 2, No. 3, in order to be more easily 
comprehended, (as otherwise, it is not necessary ;) let ah c d e f 
on the top of the plank, be the rake formed by the face-mould, the 
point g being in the line H E, and the line g e, making the same 


41 


angle with g E as the line g e, fig. 2, No. 3, makes with g k, draw 
g K, making the angle H g K equal to the angle H k K, or H i 1, 
or H p P, fig. 2, No. 3, cutting the arris, fig. 3, No. 1, G F, at K, 
then the same mould being drawn on the under side, with the point 
g at K, and the chord e g making the same angle with K F, that 
e g, on the upper side, makes with g E, or the distance of the point e 
from G F, on the lower side, equal to the distance of the point e 
from H E, on the upper side. Let us now suppose lines drawn in 
the above manner upon the three corresponding surfaces of the. 
plank to that of the figure, and let the plank be cut out with a bow 
saw. In the act of cutting, the kerf must be kept close to the cor¬ 
responding lines of each rake, and the line of the teeth of the saw 
parallel to g K, and when the piece of the wreath is entirely divested 
of the superfluous wood, the sides thus formed will be plumbed. 

To draw the Rake upon the Plank in every Position to the 
adjoining arris of the Edge. —Let fig. 3, No. 2, be a development 
of the plank as before, the same letters referring to the same parts. 
Let abcdefg be the rake drawn by the face-mould, the point g 
being in the arris H E, and the chord g e forming any given angle 
with the arris H E, less than that formed in No. 1, fig. 3, by the 
chord g e, and the arris H E ; find g as before from No. 3. In 
No. 3, draw g I, making the same angle with the pitch line g k, as 
g e makes with g E, in fig. 3, No. 2, drawg- L perpendicular to 
H E, cutting the lower arris G F in L ; make the angle K L g equal 
to the angle eg I, fig. 2, No. 3 ; make L g equal to L K ; through 
g draw M N, parallel to G F ; then drawing the rake upon the 
lower side by the edge of the mould, so that the angle e g N, on the 
said lower side, may be equal to the corresponding angle e g E, on 
the upper side ; the two sides of the piece that is to form the wreath 
may be plumbed as before, so as to correspond with the plan when 
set to its position. 

If it is required to draw the rake with each extremity of the con¬ 
cave side of the mould in the arris of the plank as in fig. 3, No. 3, 
it is only making the angle K L g equal to the angle e g k, fig. 2, 
No. 3 ; the rest is drawn, and the plumb side is formed in the same 
manner as No. 1 and No. 2. fig. 3, which suppose to be done, bend 
the corresponding part of the falling mould, fig. 2, No. 2, round the 
convex side of the piece for the wreath ; bring the points X and J 
to the plane at the top, and draw the line of support at the upper 
extremity upon the end of the wreath ; now, bring the upper end 
of the falling mould close to the extremity of the line of support, and 
draw a line by the upper edge of the falling mould ; cut away the 
superfluous wood in the manner before described, and this will form 
the back or top of the rail; then guage the two vertical surfaces to 
the same breadth, and cut the superfluous wood away from the 
under side ; this portion of the rail will then be squared. The 
wreath for the other portion above, is identically of the same form ; 
therefore, if two pieces are prepared by the same moulds and levels, 
then supposing one of these wreathed pieces to be set in its position 
for the lower part, and let the upper part be set in the same position, 


42 


and then inverted, so that the top and bottom ends, and the upper 
and lower winding - surfaces, will have changed places, but each of 
the vertical surfaces kept still upon the same side ; let the lower end 
of the higher piece be brought to contact with the higher end of the 
lower piece, that the two planes may coincide and form a joint; the 
helical solid for half a revolution will be formed out of a straight 
plank, as required to be done. 

The two wreathed portions of a hand-rail are not always alike, as 
in the preceding example ; this may happen in different ways, as 
from one quarter of the semi-circular part being divided into winders, 
and the other undivided, or, from the rail being placed higher upon 
the winders than over the flyers ; but in whatever way the variation 
takes place, the application of the principle is the same ; it only re¬ 
quires moulds to be constructed for every such variation, or separate 
part. 

The intricacy of the diagrams constructed upon the inventor’s 
former principles, prevented their being generally understood, and 
very few could practice with success. But the principles here laid 
down, are so invariable in their result, so simple and expeditious in 
their application, and so easily to be comprehended, even by a mode¬ 
rate capacity, that they cannot fail of being introduced into general 
use. They unite the requisite properties of saving labor and stuff, 
the workman constructs his moulds with ease, and has less super¬ 
fluous wood to remove. The edge of the plank is kept square, which 
entirely supersedes the bevelling, and is even in this point attended 
with a considerable saving of stuff and time, as it allows sufficient 
wood at the ends to make the heading joints, and as the piece which 
is cut out of the rail piece from the hollow side, may be turned into 
use ; but if the edge of the plank were bevelled, it would require to 
be much longer, in order to form the heading joints, and the piece 
cut out would be too trifling to be employed to any purpose. 

In addition to the advantages already enumerated, the workman 
will be encouraged by the clearness of the different steps of the 
process, which cannot fail of fully satisfying his mind as to the final 
result. 

It is likewise a great accommodation, that any rail whatever may 
be cut out of the same thickness of plank, and that the mould may 
be applied in any direction which the workman pleases to the sur¬ 
face, in order to save wood or match the fibres at the joint. 

The art of forming hand-rails round circular or elliptic well-holes, 
without the use of a cylinder, is entirely new. 

Price, the author of the “ British Carpenter ,” is the first person 
who seems to have had any idea of this art; the subsequent writers 
following his schemes, which were very uncertain in their applica¬ 
tion, have added nothing to the subject, but have even thrown it 
into greater obscurity. 

The first successful method of squaring the wreath or twist, was 
invented and published in the “Carpenter's Guide” in 1792 ; and 
certainly was the first wherein the process was subjected to any 
thing like geometrical principles, from which the result was attended 


43 


with success. In the “Carpenter's Guide," (generally called simply 
“The Guide") the formation of the face-mould was regulated by 
the falling mould or the development of the rail, not by the rise and 
tread of the steps, as shewn by Price and his followers. When the 
back or upper surface of the rail had a considerable concavity, as in 
the case of junction of flyers and winders, the consequence of this 
regulation in many cases, in the formation of the rail, was the saving 
of seven or eight inches in the thickness of stuff; and thus, while 
the method laid down by Price required a plank from six to nine 
or ten inches in thickness, according to the degree of concavity ; 
that in “the Guide" seldom required a plank more than three inches 
thick, excepting in small well-holes of three or four inches in 
diameter. 

From the great thickness of stutf to cut through, and the quantity 
to be taken away, the time required to form the piece of wood into 
a wreath by Price’s method, must have been at least double to that 
in “the Guide" and proportionally more so, as the thickness of the 
plank required by Price, was greater than that in “ the Guide" 

But though considerable advantages were thus obtained in the 
saving of stuff and labour, it must be observed, that an elevation of 
the supposed vertical ends of the twisted piece at each joint, and a 
vertical section of the said piece, were employed to obtain the in¬ 
clination of the plane of the face of the mould, or that of the faces 
of the plank ; this inclination was only correct when the planes of 
the faces of the plank were at right angles with the chord plane, or 
that passing through the chord of the plan of the wreath ; but when 
inclined to the chord plane, required thicker stuff, in proportion to 
the degree of obliquity, whether more acute or more obtuse. 

The method shewn in “ the Guide" was also the first attempt to 
spring the plank, that is, to make its plane rest upon three parts of 
the rail; and though the utmost degree of perfection was not attained, 
it has been of great use to workmen, as all the hand-rails of stairs in 
and about London, and in most parts of England, have been exe¬ 
cuted upon its principles for upwards of thirty years. 

To obtain still greater correctness, the inventor tried another 
method, by setting up three heights, supposed to be on the surface 
of a curved prism, in the middle of the rail; but this, though still 
nearer than that published in “the Guide" did not give him entire 
^tisfaction ; for the resting points being in the middle of the rail, 
the plane of section which formed the face-mould did not clear all 
the three sections without cutting into the solid of the wreath. 

In the pursuit of truth, he was led to consider what would be the 
real resting points. It readily appeared, that a level line drawn 
towards the axis of the well-hole, might be made to coincide in every 
part with the top of the rail; that if the plane of the top of the plank 
be supposed to be placed on three vertical sections of the supposed 
rail in contact with a point in each, or coincident with the whole 
line of support of one of the sections, and with a point in each of the 
other two ; and the surface of the plank thus inclined be supposed 
to be prolonged, to intersect the horizontal plane of the base, the 


44 


intersection would always point out the resting points, and shew 
their true seats upon the plan. From this consideration, it was evi¬ 
dent that the resting point of each section, and consequently each 
seat, was that extremity of each section next to the intersecting line 
of the plane of the plank and that of the plan. 

This theory being applied to practice, has given the utmost satis¬ 
faction, both in the saving of stuff and time ; the diagram for the 
face-mould is completely divested of all cross and oblique lines, and 
is, perhaps, in the most simple form to which it can possibly be re¬ 
duced ; the plane of section comes in contact with the tops of three 
vertical sections of the rail in every case whatever, and thus every 
desideratum is obtained by the most simple means. 

Therefore, in practice, if we suppose the section of the rail to be 
two and a quarter inches horizontally in breadth, and two inches in 
thickness, (as is generally the case,) a plank of two and a half inches 
thick will be sufficient for a rail, with any degree of concavity or 
convexity on the back. 

« .(From Mr. Nicholson.) 





































PI.14 


Fid / { 









































































































45 


PL. 14. 

We shall now proceed to the illustration of the subject by the 
figures which represent the solids themselves :— 

B Fig. 1, is a plan of the cylinder, with the elevation of the helical 
line, which is found by dividing the height into equal parts, and the 
circumference of the base into equal parts also, then drawing the 
lines through the points of division, as in the figure. 

Fig. 2, a representation of the solid helix twisting round the 
cylinder, making a continued rail upon a circular plan ; the curva¬ 
ture of the solid helix is, therefore, every where the same. The 
rail is exhibited as squared ; and though it appears as one piece, 
it must be understood to consist of several wreaths, or lengths, 
screwed together, each length answering to a quadrantal part of the 
plan. 

Fig. 3, shews the different sections of a hollow cylinder, cut en¬ 
tirely through the curved surface ; the solid exhibits a portion of 
the said cylinder contained between two parallel planes : INo. 1, 
shews the thickness of the section according to the inclination of the 
cutting plane; No. 2, shews the section of a semi-cylinder; and 
No. 3, that of an entire cylinder, cut according to the position of 
No. 1 ; the sections No. 2, and No. 3, being turned round, so that 
the plane of section may be brought into view, in order to make the 
solid appear. 

Fig. 4, exhibits a solid section of a hollow cylinder, upon a quad¬ 
rantal plan, with a small part straight; No. 1, exhibits the convex 
side, No. 2, the concave side. This figure shews the state of the 
rail-piece, as prepared by the face-mould, and is therefore bounded 
by two concentric cylindrical surfaces, and two parallel planes. 
The falling mould being applied upon the convex side, the super¬ 
fluous wood is cut away according to a line drawn by the upper 
edge of the falling mould, in such a manner that the stock of the 
square, being applied upon the convex side, parallel to the a,xis, the 
under edge of the blade may coincide with the top or winding sur¬ 
face of the rail-piece. The thickness of the rail is regulated by run¬ 
ning the stem of a guage first upon the convex side, with the head 
upon the top or winding surface, and then the stem upon the con¬ 
cave side in the same manner, and cutting away the superfluous 

stuff between the two guage lines. 

Fie. 5, exhibits the wreath, or rail-piece, as completely squared ; 
No. f, shews the concave side, with the lower end of the back, or 
upper surface, and the higher end of the lower surface *, and No. 2, 
the convex side of the cylindric surface, with the upper part of the 
back, and the lower part of the under side. . 

The rail exhibited in fig. 2, is only a succession of wreaths, as in 

^From what has been shewn, it will be easy to conceive how a rail 
may be executed to any given plan, and to any development of the 
steps according to that plan. 


46 


Though it may be possible to make a rail in one piece, as in fig. 3, 
No. 3, such a rail will hardly ever come into practice ; the repre> 
sentations of the solid sections, in Nos. 2 and 3, are therefore not 
shewn with a view of being prepared for a rail, but to give a clear 
view of the different parts of the solid sections of a hollow cylinder. 


(From Mr. Nicholson.) 





























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PI. 15 























































47 


PL. 15. 

This Plate is introduced to explain the most ready method of 
construction for the framing and applying the common carriages 
of a winding stair-way, in which, very frequently, materials and 
and labor are unnecessarily applied. The application and location 
of the several carriage pieces will be governed by the judgment 
of the workman. The following description will serve as a general 
rule, and in most instances answer with a decree of perfection. 

Fig. 1, Plan of a portion of the stair, showing the different parts, 
as at the letters. 

a, the front string. 

b b b, &c., the plans of the common timber carriages thrown in, 
as most convenient for the winders, &c. 

c c c, the under line of the steps and risers in the elevation oibbb. 
The dotted lines represent the steps and risers. The carriages b b b, 
are of scantling, about 4-S, and are cut off on the under side, when 
they may drop below the soffet or plastering of the stair. 

The executor will readily perceive that a line running diagonally 
across the steps will vary the widths, and consequently require each 
one to be raised from its plan, as in c c c from b b b. 


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